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The paper suggests the use of Multi-Valued Decision Diagrams (MDDs) as the supporting data structure for a generic global constraint. We give an algorithm for maintaining generalized arc consistency (GAC) on this constraint that amortizes…
An algorithmic proof of the General N\'eron Desingularization theorem and its uniform version is given for morphisms with big smooth locus. This generalizes the results for the one-dimensional case.
The \emph{Order-Maintenance} (OM) data structure maintains a total order list of items for insertions, deletions, and comparisons. As a basic data structure, OM has many applications, such as maintaining the topological order, core numbers,…
Graph condensation (GC) aims to distill the original graph into a small-scale graph, mitigating redundancy and accelerating GNN training. However, conventional GC approaches heavily rely on rigid GNNs and task-specific supervision. Such a…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital…
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…
Traditionally, different types of feature operators (e.g., convolution, self-attention and involution) utilize different approaches to extract and aggregate the features. Resemblance can be hardly discovered from their mathematical…
Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has…
In this paper, we present a unified framework for studying cohomology theories of various operators in the context of pseudoalgebras. The central tool in our approach is the notion of a quasi-twilled Lie pseudoalgebra. We introduce two…
We consider regenerating codes in distributed storage systems where connections between the nodes are constrained by a graph. In this problem, the failed node downloads the information stored at a subset of vertices of the graph for the…
We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this…
In this expository paper we give an elementary, hands-on computation of the homology of the little disks operad, showing that the homology of a $d-fold loop space is a Poisson algebra. One aim is to familiarize a greater audience with…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
Recently it has been shown that computing the dimension of the first homology group $H_1(K)$ of a simplicial $2$-complex $K$ embedded linearly in $\mathbb{R}^4$ is as hard as computing the rank of a sparse $0-1$ matrix. This puts a major…
In a previous work a procedure was decribed for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the building of a combinatorial structure from data…
The goal of this article is to relate recent developments in cyclic homology theory with the theory of operads and homotopical algebra, and hence to provide a general framework to define and study operations in cyclic homology theory.
Sampling is a widely used graph reduction technique to accelerate graph computations and simplify graph visualizations. By comprehensively analyzing the literature on graph sampling, we assume that existing algorithms cannot effectively…
Expanders are powerful algorithmic structures with two key properties: they are a) routable: for any multi-commodity flow unit demand, there exists a routing with low congestion over short paths, where a demand is unit if the amount of…
Multi-class segmentation of cardiac magnetic resonance (CMR) images seeks a separation of data into anatomical components with known structure and configuration. The most popular CNN-based methods are optimised using pixel wise loss…